Quadratic spaces over discrete Hodge algebras
type: Item
instance of: scholarly article
title: Quadratic spaces over discrete Hodge algebras
zbMATH Open document ID: 0603.13011
DOI: 10.1016/0022-4049(86)90093-9
published in: Journal of Pure and Applied Algebra
publication date: 1986-01-01T00:00:00Z
review text: A and R are commutative Noetherian rings with 2 invertible; R is a ''discrete Hodge algebra'' over A if \(R\cong A[X_ 0,...,X_ n]/I\) for an ideal I generated by monomials. Theorem 1: If A is a Dedekind domain, any quadratic space over R which contains a unimodular isotropic element comes by base extension from A. Theorem 2: Let q be a quadratic space over R and assume Witt index of \(q\geq \dim R>\dim A,\) then q is cancellative. These theorems generalize results of \textit{R. Parimala} [Am. J. Math. 103, 289-296 (1981; Zbl 0466.13007) and Commun. Algebra 12, 229- 238 (1984; Zbl 0532.10015)].
Mathematics Subject Classification ID: 13C13
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 11E16
zbMATH DE Number: 3973011
zbMATH Keywords: discrete Hodge algebra
zbMATH Keywords: quadratic space
zbMATH Keywords: Witt index
author: Satyagopal Mandal
reviewed by: Charles Small
MaRDI profile type: Publication
full work available at URL: 0022-4049(86)90093-9
OpenAlex ID: W1994791662
cites work: Some results about modules over discrete Hodge algebras
cites work: Introduction to Algebraic K-Theory. (AM-72)
cites work: Quadratic Forms Over Polynomial Rings Over Dedekind Domains
cites work: Cancellation of quadratic forms over polynomial rings
cites work: Extendability of quadratic modules with sufficient Witt index. II
cites work: Cohen-Macaulay quotients of polynomial rings
cites work: Cancellation of quadrate forms over commutative rings
cites work: Q3310743
cites work: The Serre problem for discrete Hodge algebras
description: scientific article; zbMATH DE number 3973011